BRIDGEPORT — Already shooting for the moon, city Board of Education members have decided to reach for some stars as well.

The go-for-broke attitude comes from members of the board’s finance committee who are poised to ask a deficit-plagued state and a city with a shrinking grand list to give it as much as $21.1 million more next year.

“We need a number that says ‘this is what it would take,’ ” said Howard Gardner, chairman of the committee. “We just have to do it ... Let’s put it out there and let’s talk about it.”

Interim Schools Superintendent Fran Rabinowitz maintains that $15.1 million more is needed than the district’s 2015-16, $245 million operating budget, just to offer what the district does now, due to rising costs and a growing student population.

The remaining $5 million to $6 million would provide services to help underperforming students by providing extra reading help at the high school, more behavior and academic support, classroom aides in kindergarten classes and an expanded music and middle school sports program.

The request, which goes to the full school board on Monday, would push the district’s operating budget 8.5 percent above its current level. Last year, the district asked for a $7 million increase and got about $4.8 million more, between the city and state.

This year, under Gov. Dannel P. Malloy’s budget, the district would be flat funded and would see decreases in several grants it has come to rely upon. The city, meanwhile, is facing a $20 million budget shortfall this year, according to Mayor Joseph Ganim, and just learned its grand list from which tax revenues are generated has shrunk by 15 percent.

The school district’s proposed 2016-17 spending plan assumes an enrollment increase of 428, giving the district 21,478 students next year. The district currently spends $13,923 per student, the board was told, about $5,000 fewer than Westport and $6,000 fewer than Hartford.

Gardner said there is a case to be made for additional funding, if it can turn the system around.

“If we are going to move this district forward ... I think that people will open up the pocketbook or make some sacrifices in other areas of the city budget, if we say look, ‘This is key,’ ” he said.

Maria Pereira, another school board member, said if enough is invested in education, money would be saved in police cost, court costs and incarceration costs.

Rabinowitz said she had no problem asking for what is needed. In the past year, she said, students have started showing academic growth, just not enough.

“If we had more intervention it would go faster,” she said.

Rabinowitz also has a plan for an in-district program for students designated as “behaviorally challenged.”

“We are identifying way too many very young children as socially and emotionally maladjusted or disturbed,” she said.

On Wednesday, Rabinowitz traveled to Hartford to pitch the idea to House Speaker Brendan Sharkey, D-Hamden. It would require $1 million to get off the ground, Rabinowitz said.

Gardner encouraged the superintendent to come back to the full board on Monday with a price tag that reflects just how many high school students in the district are behind in reading, and what it would take to get them to grade level.

“We need to say, ‘what kind of staffing do we truly need and what program?’ ” Gardner said. “I don’t want to just throw money at interventions if they aren’t (effective).”

Once the board acts on the budget, it goes to the city. A lot will also depend on the state, which funds about three-quarters of the district’s operating budget.

The district has planned three community forums to explain the plan. The first will be March 23 at Batalla School, the second on March 30 at Discovery Magnet School and the third on April 5 at Tisdale School. All three are scheduled to run from 6 to 7 p.m.